In addition to fancy controls and new content, the new versions will both feature an entirely new leveling system, with players putting points toward "Enforcer" skills or "Operator" skills. These reflect different styles of play; if you like solving problems with violence and just want to rip shit up, then the Enforcer path will make you a better fighter and give you cool new moves - like the ability to plant car bombs, for example.
But if you'd rather negotiate for what you want, then becoming an Operator will make that a lot easier. It'll also net you more money and respect, and will enable you to call in the new Corleone hit squads more often. Where the Xbox 360 version let you hire a single Corleone sidekick, the new versions enable you to whistle up four guys of varying strength - in addition to your paid henchman - to watch your back until they're dead.